# Properties

 Label 1386.2.w Level $1386$ Weight $2$ Character orbit 1386.w Rep. character $\chi_{1386}(353,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $160$ Sturm bound $576$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1386.w (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$63$$ Character field: $$\Q(\zeta_{6})$$ Sturm bound: $$576$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1386, [\chi])$$.

Total New Old
Modular forms 592 160 432
Cusp forms 560 160 400
Eisenstein series 32 0 32

## Trace form

 $$160q - 160q^{4} - 4q^{7} - 8q^{9} + O(q^{10})$$ $$160q - 160q^{4} - 4q^{7} - 8q^{9} - 12q^{13} + 12q^{14} + 28q^{15} + 160q^{16} + 36q^{17} + 8q^{18} + 4q^{21} - 24q^{23} - 80q^{25} - 36q^{27} + 4q^{28} - 12q^{29} + 8q^{36} + 4q^{37} + 4q^{39} + 12q^{41} + 4q^{43} + 12q^{45} - 12q^{46} + 72q^{47} + 16q^{49} - 24q^{50} - 8q^{51} + 12q^{52} + 48q^{53} - 36q^{54} - 12q^{56} - 16q^{57} - 28q^{60} - 72q^{62} - 92q^{63} - 160q^{64} + 56q^{67} - 36q^{68} + 84q^{69} + 24q^{70} - 8q^{72} - 36q^{74} + 36q^{75} + 8q^{79} + 40q^{81} - 4q^{84} - 24q^{86} + 36q^{87} - 12q^{89} - 36q^{90} + 24q^{91} + 24q^{92} + 56q^{93} - 12q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1386, [\chi])$$ into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

## Decomposition of $$S_{2}^{\mathrm{old}}(1386, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1386, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(63, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(126, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(693, [\chi])$$$$^{\oplus 2}$$